Fraunhofer SIT Independent Linaro University of Applied Sciences Bonn-Rhein-Sieg Google LLC The Conceptual Messages introduced by the RATS architecture (RFC9334) are protocol-agnostic data units that are conveyed between RATS roles during remote attestation procedures. Conceptual Messages describe the meaning and function of such data units within RATS data flows without specifying a wire format, encoding, transport mechanism, or processing details. The initial set of Conceptual Messages is defined in Section 8 of RFC9334 and includes Evidence, Attestation Results, Endorsements, Reference Values, and Appraisal Policies. This document introduces the Conceptual Message Wrapper (CMW) that provides a common structure to encapsulate these messages. It defines a dedicated CBOR tag, corresponding JSON Web Token (JWT) and CBOR Web Token (CWT) claims, and an X.509 extension. This allows CMWs to be used in CBOR-based protocols, web APIs using JWTs and CWTs, and PKIX artifacts like X.509 certificates. Additionally, the draft defines a media type and a CoAP content format to transport CMWs over protocols like HTTP, MIME, and CoAP. The goal is to improve the interoperability and flexibility of remote attestation protocols. By introducing a shared message format like the CMW, we can consistently support different attestation message types, evolve message serialization formats without breaking compatibility, and avoid having to redefine how messages are handled in each protocol.